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A116217
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Decimal expansion of constant Sum_{i,j,k=1..inf} 1/2^(i*j*k).
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0
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2, 3, 2, 4, 7, 8, 4, 7, 7, 2, 8, 4, 0, 4, 7, 9, 0, 6, 1, 2, 3, 5, 2, 1, 7, 6, 8, 2, 8, 6, 1, 3, 9, 3, 0, 4, 6, 0, 2, 0, 9, 5, 1, 3, 4, 5, 2, 2, 5, 4, 7, 6, 0, 5, 3, 6, 0, 1, 4, 6, 9, 4, 6, 4, 4, 4, 1, 9, 2, 2, 0, 2, 0, 0, 4, 6, 3, 9, 7, 7, 0, 3, 1, 7, 3, 6, 9, 8, 8, 4, 0, 1, 5, 1
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) is decimal expansion of constant that is a sum of triple series Sum[Sum[Sum[1/2^(i*j*k),{i,1,Infinity}],{j,1,Infinity}],{k,1,Infinity}] = 2.3247847... It is similar to Erdos-Borwein constant Sum[Sum[1/2^(i*j),{i,1,Infinity}],{j,1,Infinity}] = Sum[1/(2^k-1),{k,1,Infinity}] = 1.60669515...
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LINKS
| Eric Weisstein's World of Mathematics, Triple Series.
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FORMULA
| Equals sum_(n=1..infinity) A007425(n)/2^n . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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EXAMPLE
| 2.32478477284047906123521768286139304602095134522547605...
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PROG
| (PARI): /* Using sum(n=1..infinity, A007425(n)/2^n ) */
lambert2ser(L)=
{
local(n, t);
n = length(L);
t = sum(k=1, length(L), O('x^(n+1))+L[k]*'x^k/(1-'x^k) );
t = Vec(t);
return( t );
}
N=1000; v=vector(N, n, 1); /* roughly 1000 bits precision */
t=lambert2ser(lambert2ser(v)); /* ==[1, 3, 3, 6, 3, 9, ...] == A007425 */
default(realprecision, floor(N/3.4)); /* factor approx. log(10)/log(2) */
sum(n=1, #v, 1.0*t[n]/2^n)
/* == 2.324784772840479061235217682861... */
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CROSSREFS
| Cf. A065442 = Decimal expansion of Erdos-Borwein constant Sum_{k=1..inf} 1/(2^k-1).
Sequence in context: A079159 A192298 A132439 * A108838 A105070 A154578
Adjacent sequences: A116214 A116215 A116216 * A116218 A116219 A116220
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KEYWORD
| cons,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 09 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2008
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